Answer
$\frac{8}{9}i+\frac{-1}{9}j+ \frac{4}{9}k$
Work Step by Step
Let $\mathbf v=8i-j+4k$. We can obtain a unit vector in the same direction as $\mathbf v$ by multiplying $\mathbf v$ by $\frac{1}{|\mathbf v|}$.
By definition, $|\mathbf v|=\sqrt{8^2+(-1)^2+4^2}=\sqrt{64+1+16}=\sqrt{81}=9$.
So $\frac{\mathbf v}{|\mathbf v|}=\frac{\mathbf v}{9}=\frac{8i-j+4k}{9}= \frac{8}{9}i+\frac{-1}{9}j+ \frac{4}{9}k$ is a unit vector in the same direction as $\mathbf v$.